Complexity spectrum: Difference between revisions

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: This revision was by author [[User:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-06-~~28 03~~:08:53 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-13 13:02:18 UTC</tt>.<br>

: The original revision id was <tt>~~239087885~~</tt>.<br>

: The original revision id was <tt>274836228</tt>.<br>

: The revision comment was: <tt></tt><br>

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<h4>Original Wikitext content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q [[odd limit]] [[tonality diamond]] between the unison and half an octave, where q is two less than the next prime after p. In the rank two case, the complexity is [[Graham complexity]], but for higher limits we can use [[Tenney-Euclidean metrics|OE complexity]], which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q [[odd limit]] [[tonality diamond]] between the unison and half an octave, where q is two less than the next prime after the prime limit of the temperament in question. In the rank two case, the complexity is [[Graham complexity]], but for higher limits we can use [[Tenney-Euclidean metrics|OE complexity]], which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.

The different flavors of a temperament, so to speak, are shown in its spectrum. A temperament like meantone, which favors 3 over 5, and 5 over 7, has quite a different flavor than miracle, which favors 7, 11/9 and 7/5.

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Even leaving aside the somewhat greater complexity and accuracy, it just won't taste the same.</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Spectrum of a temperament</title></head><body>One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q <a class="wiki_link" href="/odd%20limit">odd limit</a> <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> between the unison and half an octave, where q is two less than the next prime after p. In the rank two case, the complexity is <a class="wiki_link" href="/Graham%20complexity">Graham complexity</a>, but for higher limits we can use <a class="wiki_link" href="/Tenney-Euclidean%20metrics">OE complexity</a>, which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.<br />

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Spectrum of a temperament</title></head><body>One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q <a class="wiki_link" href="/odd%20limit">odd limit</a> <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> between the unison and half an octave, where q is two less than the next prime after the prime limit of the temperament in question. In the rank two case, the complexity is <a class="wiki_link" href="/Graham%20complexity">Graham complexity</a>, but for higher limits we can use <a class="wiki_link" href="/Tenney-Euclidean%20metrics">OE complexity</a>, which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.<br />

<br />

The different flavors of a temperament, so to speak, are shown in its spectrum. A temperament like meantone, which favors 3 over 5, and 5 over 7, has quite a different flavor than miracle, which favors 7, 11/9 and 7/5.<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-28 03:08:53 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-13 13:02:18 UTC</tt>.<br>
-: The original revision id was <tt>239087885</tt>.<br>
+: The original revision id was <tt>274836228</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q [[odd limit]] [[tonality diamond]] between the unison and half an octave, where q is two less than the next prime after p. In the rank two case, the complexity is [[Graham complexity]], but for higher limits we can use [[Tenney-Euclidean metrics|OE complexity]], which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q [[odd limit]] [[tonality diamond]] between the unison and half an octave, where q is two less than the next prime after the prime limit of the temperament in question. In the rank two case, the complexity is [[Graham complexity]], but for higher limits we can use [[Tenney-Euclidean metrics|OE complexity]], which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.
 The different flavors of a temperament, so to speak, are shown in its spectrum. A temperament like meantone, which favors 3 over 5, and 5 over 7, has quite a different flavor than miracle, which favors 7, 11/9 and 7/5.
@@ Line 22: / Line 22: @@
 Even leaving aside the somewhat greater complexity and accuracy, it just won't taste the same.</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Spectrum of a temperament&lt;/title&gt;&lt;/head&gt;&lt;body&gt;One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q &lt;a class="wiki_link" href="/odd%20limit"&gt;odd limit&lt;/a&gt; &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; between the unison and half an octave, where q is two less than the next prime after p. In the rank two case, the complexity is &lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;, but for higher limits we can use &lt;a class="wiki_link" href="/Tenney-Euclidean%20metrics"&gt;OE complexity&lt;/a&gt;, which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Spectrum of a temperament&lt;/title&gt;&lt;/head&gt;&lt;body&gt;One of the things one can look at when analyzing a temperament is its complexity spectrum. This may be defined as the result of sorting the complexity of the intervals in the q &lt;a class="wiki_link" href="/odd%20limit"&gt;odd limit&lt;/a&gt; &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; between the unison and half an octave, where q is two less than the next prime after the prime limit of the temperament in question. In the rank two case, the complexity is &lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;, but for higher limits we can use &lt;a class="wiki_link" href="/Tenney-Euclidean%20metrics"&gt;OE complexity&lt;/a&gt;, which is proportional to Graham complexity in the rank two case, but is also valid for higher limits.&lt;br /&gt;
 &lt;br /&gt;
 The different flavors of a temperament, so to speak, are shown in its spectrum. A temperament like meantone, which favors 3 over 5, and 5 over 7, has quite a different flavor than miracle, which favors 7, 11/9 and 7/5.&lt;br /&gt;